5/05/2016

In a former life, I was a mathematician. I used to maintain a weblog called The Unapologetic Mathematician — a winking allusion to G.H. Hardy's much more famous A Mathematician's Apology. And yes, I know that Hardy meant his title more in the sense of an explanation or defense, as in theology.

Point being, where most kids grow up hearing stories about — I don't know, sportsball players or something — I grew up with John Nash, Alan Turing, and Srinivasa Ramanujan. And Ramanujan was always the most alien to my sense of what mathematics was. Not because he was from India, but because he produced thousands of mostly number-theoretic and analytic identities, seemingly from thin air.

In some sense, each of these identities just gives two different calculations and says that they both give the same answer. Like when we say multiplication is commutative: given two whole numbers like three and four we can lay out a rectangular grid of stones and count them up. Whether we group them as three rows of four stones, or as four columns of three stones, we get the same number either way, and so on for any other numbers we might have picked. Ramanujan, teaching himself mathematics from second-hand textbooks, came up with fantastically complicated identities I won't even try to write down here.

They were so unexpected that when Hardy (the same one from the Apology) received them in the mail, he was dumbfounded. Some of them looked at least plausible, but some Hardy couldn't even guess why they might be true. And yet they were too weirdly specific to be the sort of thing someone would just make up. Two other Cambridge mathematicians had already returned the packet of loose-leaf notes as the work of a crank — trust me, you get plenty even when you're a lowly instructor — but Hardy started a correspondence that eventually brought Ramanujan to work with him and J.E. Littlewood.

The Man Who Knew Infinity gets at least the facts of his mathematical life correct. Ramanujan (Dev Patel) starts out in 1913, struggling to find a clerkship in Madras. It's left unsaid, though, that the reason he lacks a degree is mostly his own inattention to any subject other than mathematics, rather than some sort of discrimination against him. He was, after all, a Brahmin, at the top of the caste system that still existed under the British Raj. That's also why, after Hardy (Jeremy Irons) invites him to study at Cambridge, his mother objects: going abroad is low-class, and forbidden to a Brahmin.

Upon his arrival, Ramanujan is given a wake-up call by Hardy and Littlewood (Toby Jones). Simply plucking his identities out of thin air and writing them down won't fly here. Academic mathematics is organized around the notion of proofs, which at the time were thought of as formal, rigorous methods of establishing truth. Intuition could serve to generate targets — whether it came from Hardy's broad contextual background in academic mathematics or Ramanujan's dreams of his local deity of Namagiri — but it must be backed up with step-by-step proof.

I don't really expect that any movie could delve into the weeds of mathematical epistemology, sussing out the distinctions between an intuition-driven mathematics and and a proof-based one, much less the complicated ways they interact with the then-ongoing philosophical battle between Platonism and Formalism. The former holds, as Ramanujan puts it, that a meaningful mathematical statement expresses "a thought of God", while the latter sees mathematics as a game that cranks out new results as long as you follow the rules carefully. Most in the audience won't care, and to get any sort of resolution would require decades more of the story.

Instead, it settles on the simpler, more romantic conflict between Ramanujan's faith and Hardy's atheism which, though palatable to a wide Western audience, has the small drawback of being wrong. Ramanujan was clearly informed by the culture he grew up in, and was a conscientious practitioner to the extent it didn't get in the way of his mathematical studies. So conscientious, in fact, that his strict vegetarianism likely led to malnutrition that led to a recurrence of the amoebiasis endemic to Madras that was misdiagnosed in England — and in the script — as tuberculosis. But he also said that all religions seemed about equally true, and there was hardly an obstacle to his work with Hardy over the issue.

That the movie oversimplifies the mathematical ideas Ramanujan explored is understandable, even when it leads to getting things flat-out wrong for the sake of dramatic exposition. He never claimed an exact calculation of the prime-number-counting function; only refinements of estimates that Hardy was certainly well-acquainted with and would hardly have been shocked to see. His work on partition-counting, though fascinating, was not a foundational as presented. But it does set up the right interactions with other Cambridge faculty to illustrate how Ramanujan was received.

But rounding off these corners to widen the audience leads to replacing the less-accessible drama of mathematics with the cheaper melodrama of a conflict between his wife (Devika Bhise) and his mother (Arundathi Nag), who hides his wife's letters so they won't distract him from his work. Work which, per the movie, she didn't want him to leave for in the first place. The casting also rounds off the uncomfortable fact that Ramanujan's wife was 13 or 14 when he left, and she joined him in Madras at the start of the movie not because he'd finally obtained a job, but because she'd finally started her adolescence.

In its outlines, The Man Who Knew Infinity does a good job of giving the facts of Ramanujan's life even as it massages them into an audience-friendly form. The best writing, though, goes to Hardy, or maybe it's Irons' deft performance. It would have been easy to let him become the standard Good White Guy who comes to the story without racism, but Irons lets him be sympathetic without being perfect. This version of Ramanujan, on the other hand, is the same excitable, socially awkward, borderline-autistic character Patel goes back to again and again. I can walk away from the movie with a good thumbnail sketch of his life, but I hardly feel like I understand the man himself.